Some Theorems on Fixed Points Set of Asymptotically Demicontractive Mappings in the Intermediate Sense
A. S. Oke *
Department of Mathematical Sciences, Faculty of Science, Adekunle Ajasin University Akungba Akoko, Ondo State, Nigeria.
D. J. Kayode
Department of Mathematical Sciences, Faculty of Science, Adekunle Ajasin University Akungba Akoko, Ondo State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we establish the closedness and convexity of the fixed point set of asymptotically demicontractive mappings in the intermediate sense introduced by Olaleru and Okeke [Convergence theorems on asymptotically demicontractive and hemi-contractive mappings in the intermediate sense. Fixed Point Theory and Applications 2013, 2013:352]. We also establish the equality of the fixed point set and asymptotic fixed point set.
Keywords: Convex sets, demiclosed, demicontractive mappings in the intermediate sense, fixed point set, asymptotic fixed point set.